Tuesday, December 6, 2016

Iced Tea

Sometimes my sister will put an ice cub into her tea to make it cool enough to drink right after she makes it. I wanted to know if you put an ice cube into a hot cup of tea, how much does the temperature actually decrease?

A typical ice cube is 10 g (or 0.01 kg) and the specific heat for ice is 2100J/K°C. A cup of tea (just water- we’ll assume the tea bag has been removed) is 225g (or 0.225 kg) and the specific heat for water is 4186 J/K°C.

We can assume the initial temperate of the ice is 0°C, and the initial temperature of the tea is 90°C (it was just boiling). Therefore we can solve for the change in T:

The specific heats are the same for water in each case, so the c’s cancel out.
The temperature of the tea decreases by only 0.9°C.

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